ML20236A912

Criticality Safety Evaluation of Boraflex Degradation in Quad Cities Spent Fuel Storage Racks

ML20236A912
Person / Time
Site:	Quad Cities
Issue date:	06/30/1987
From:	Sarah Turner BLACK & VEATCH
To:
Shared Package
ML20236A865	List: ML20236A863 ML20236A912 ML20236A929
References
SS-167, NUDOCS 8707280268
Download: ML20236A912 (39)

Text

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ .-_ _ . _ _ _ . _ _ _ _ _ _ _ - _ - _ _ _ _ _ _ _ _ _ _____

1 SS-167 l

l l e l

i I

l CRITICALITY SAFETY EVALUATION OF BORAFLEX DEGRADATION IN THE QUAD CITIES SPENT FUEL STORAGE RACKS Prepared for the COMMONWEALTH EDISON COMPANY by Stanley E. Turner, Ph.D., P.E.

With Supplement by Northeast Technology Corporation Report NET-044-1 June 1987 a SOUTHERN SCIENCE

- OFFICE OF BLACK & VEATCH POST OFFICE BOX 10. DUNEDIN, FLORIDA 33579 - B13/733-3138 B707260260 07072g DR ADOCK 05000254 l l

PDR l

- _ _ _ , _ - - _ -----r-- ----,-,, , - - - . .___ ___ __ __ , _ _ _ _ _ _ _

al ,

b. -

.j E*

J

( l \

V d P i E

b TAbiE OF CONTENTS j

l. t 1;

=l l

' 'Page i 1.0 INTRODUCT10N...................................... l'

SUMMARY

hND CONCLUSIONS........................... 2

2. 0' 8 l 3.0- ANALYTICAL METHODOLOGY............................ l Fuel Assembly................................ 8 3.1 Storage Reck Design........................... 8 3.2 1 3.3 Geometric Model.............................. 11 3.4 Calculational Model.......................... 14 RESULTS.........................,... 3............ 16 4.0 4.1 Fuel Burnup Calculations..................... 16 4.2 Two-Dimensional PD07 Calculations............ 18 4.3 Three-Dimensional Synthesis.................. 20 4.4 Uncertainties in Criticality Calculations. . . . 21  !

. 4. 5 Capability of Fuel Storage Rack.............. 25 REFERENCES APPENDIX A NORTHEAST TECHNOLOGY CORPORATION REPORT NET-044-1:

AN ASSESSMENT OF BORAFLEX GAP DISTRIBUTIONS IN THE QUAD CITIES SPENT FUEL STORAGE RACKS l

1 1 1 l

11 4

,1 ',

$ 8., l?

' LIST OF. TABLES 4 e q

Page No . '

^

9

' l' . FUEL ASSEMBLY DESIGN SPECIFICATIONS..............

i- 2 PROBABILITIES' OF AXI ALLY COINCIDENT BORAFLEX 13 GAPSxIN LARGEST ( 16 BY 16 ) . MO DU LE S . . . . . . . . . . . . . . . .

3 EFFECT.0F ASSEMBLY CONFIGURATION AND AVERAGE 18. .

VOID..............................................

~4 INFINITE MULTIPLICATION. FACTORS FROM PD07 19-CALCULATIONS WITH. MISSING BORAFLEX SHEETS.........

5 THREE-DIMENSIONAL CALCULATIONS'WITH 10-INCH 21 REGIONS OF MISSING BORAFLEX.......................

6 -COMBINED UNCERTAINTIES IN CRITICALITY SAFETY 24 A ANALYSIS..........................................

7 CALCULATED k VALUES WITH BORAFLEX GAPS'IN THE 26 QUAD CITIES ETORAGE' RACKS.........................

LIST OF FIGURES 1 Maximum Reactivity (k ) .in Quad Cities fuel 5

. storage rack with postulated Boraflex gaps. . . . . . . .

2 Reactivity in fuel storage rack as a function 6 of reactivity in standard core : geometry. . . . . . . . . . .

3 Cross-section of reference design storage cell 10 for Quad Cities........'...........................

4 Cross-sectional diagram of 4 by 4 cell arrange- 12 ment for PDO calculational unit...................

5 . Typical reactivity effects'of fuel burnup on 17 Quad Cities fuel (in storage rack ) . . . . . . . . . . . . . . . .

6 Variation in rack (k,) for gap sizes up to 22 10 inches in several configurations...............

q i

4 lii

_ . . . _ . _ _ _ . _ . .. . . . .a

i O-l,

1.0 INTRODUCTION

Special tests of the Oaad Cities spent fuel ' storage racks

'recently revealed the possible existence of defects (gaps) in the j neutron absorber material (Boraflex) of the storage cells. Sub-sequent detailed evaluation confirmed that axial gans exist and identified numerous small gaps. The largest gap observed was 3 1/2 to 4 inches at two locations. The existence of these gaps is attributed to radiation-induced shrinkage and cracking of the Boraflex sheets, with the gaps occurring in various widths and at various locations in a generally random fashion. One assessment has conservatively projected the possibility of axial gaps approaching 10 inches in width as the storage cells accumulate further radiation dose. The possibility of random gaps of various lengths in the Boraflex up to and including 10 iqches was assumed for the present study, with the objective of assessing the potential impact of such gaps on the criticality safety of the Ouad cities spent fuel storage racks.

In a parallel , supporting study, the Northeast Technology Corporation has conservatively evaluated probabilities of Boraflex gaps occurring in random' sizes and locations. Their results are incorporated heroin as a supplement.

l 1

j i

____________A

O 2.0

SUMMARY

AND CONCLUSIONS The Quad Cities spent fuel storage rack consists of a series of modular honeycomb structures, containing square cells arranged on a 6.22-inch lattice spacing. Sheets of neutron absorbing material (Boraflex) are sandwiched between the stainless steel walls of adjacent storage cells. The two Boraflex sheets and nominal 3-inch water flux-trap between the outer absorber sheets of adjacent modules effectively isolates the individual modules from each other. The largest module is a 16 by 16 cell array with a total of 256 cells and 450 Boraflex sheets.

For analytical purposes, a 4 by 4 array of cells was chosen, centered around the postulated defect (s) at any given axial plane, with reflecting boundary conditions used on all sides of the array. This array is suf ficiently large to adequately repre-cent an axial plane through a storage module and is conservative since, in effect, the model replicates postulated gaps throughout the entire module. In this 16-cell calculational unit, the prob- l ability of Boraflex gape of significant size (>4 inches) existing at the same axial plane in all 24 internat sheets of the unit is l vanishingly small, being of the order of 10-24 Therefore, this calculational unit adequately and conservatively represents any

~

of the rack modules in the storage pool.

The basic calculational model used was the CASMO-2E 2-dimen-sional transport theory code for single fuel assemblies.Ill I

Equivalent diffusion theory constants, produced by CASMO, were used in 2-dimensional PDQ7(2 ) calculations of the 16-cell array, assuming various combinations of missing Boraflex sheets (assumed l to be replaced by water). Flux-weighted diffusion theory con-stants in the PD07 output edits were used in a one-dimensional axial calculation (SNEID code)(3) to syntinesize 3-dimensional calculations. Certain limiting cases described by the 3-dimen-sional synthesis were calculated ar, a full 3-dimensional array J 2

l l

using the AMPX-KENO Monte Carlo computer code package with the 27-group SCALE cross-section set. Results of these AMPX-KENO check calculations confirmed the 3-dimensional synthesis model and suggested that the synthesis model conservatively over-predicts reactivity slightly. A special calculation was made, assuming the Boraflex was missing in the top 10 inches of all cello, to confirm that the 6 inches of natural uranium fuel preclude any criticality problem at the ends of the fuel assembly. Results confirm that the combination of natural uran-ium fuel and axial neutron leekage from the ends of the active fuel more than compensates for the possible loss of the upper 10 inches of Boraflex.

Virtually an infinite combination of gap sizes and axial locations is theoretically possible. Therefore, a number of gap distributions were developed by Monte Carlo techniques and used as a basis for assigning a reactivity allowance that would cred-ibly constitute an upper bound limit. These calculations suggest that an allowance of 0.040 Ak would constitute a conservative upper bound limit to the reactivity increase due to the possible j occurrence of 10-inch gaps in the Boraflex absorber. This allow- f ance is equivalent to 10-inch gaps in approximately 10 adjacent I

sheets at the same axial plane (occurrence probability of ~10-28 or of gaps of 4 inches occurring at the same axial elevation in all sheets (occurrence probability of ~10-82),

The CASMO-PDQ7-SNEID calculational methodology was thus used  !

I solely to determine the upper bound uncertainty allowance for potential Boraflex gaps. This uncertainty (0.040 ak) was j combined with other uncertainties (calculational uncertainty and l manufacturing tolerances) and added to the results of CASMO-2 E calculations for various enrichment cases. Results of these calculations, which include an additive total allowance of  !

0.0529 Ak for all uncertainties, determine the maximum reactivity l in the spent fuel storage pool and allcw criteria to be defined 3

for safe storage of new 'and spent fuel assemblies. Figure 1 shows the maximum reactivity (k,) of new and spent fuel in the storage pool for enrichments up to 3.8 wt.% U-235. The same in-rack reactivity data (k,) .is shown in Fig. 2 as a function of the infinite multiplication factor (k,) of the fuel assembly in the standard

• core geometry. In both cases, fresh fuel exhibits a significantly lower reactivity provided there is at least 2.5%

gadolinium oxide (Gd 230 ) in a minimum of five (5) fuel rods of each assembly. For the Quad Cities fuel (typical GE 8 x 8 R assemblies), the limiting condition occurs for fuel of 8 Mwd /kgU, corresponding to the peak reactivity during burnup. In this case, the maximum k, of the storage rack, including uncertain-ties, with fuel of 3.8% initial enrichment is only 0.9314.

Although the criticality calculations assumed an infinite array of fuel at the burnup corresponding to the maximum reactivity (8 Mwd /kgU), in reality this burnup will occur only over a narrow axial region of the fuel assembly. Adjacent fuel of higher or lower burnup on both sides of the 8 Mwd /kgU axial region will exhibit lower reactivity since (1) lower burnup fuel will still contain gadolinium that has not yet burned out, and (2) higher burnup fuel normally has a lower reactivity.

Based upon the data and considerations discussed above, fresh or spent fuel may be safely stored in the Quad Cities spent fuel storage racks provided the following criteria are satisfied.

The average initial enrichment of the fuel is equal to or less than 3.8 wt.% U-235 (excluding the natural uranium blanket),

and either of the following:

• The " standard" core geometry is defined as fuel assemblies on a with 6-inch (core) lattice spacing in cold (68'F), clean water no void and without control absorber.

4

~

~ -

0JA) C" ES S3Y J_ RACKS 0.95 -

0.94-

^ cb' 0'93

+ /ge

&V

g. 0.93. -

0.91 A1

'O

.' y . 0.9

_ +Y

.:7 I

r 0.89 -

/ ^g ~

! g 'T

.w 0.88  ?

g 0.87 ., y+

l to o y 0.86 j-95 0.85 0.84  ;

1 l 0.83 1

3.1 3.3 3.5 3.7 3.9 ENRICHET, WI.t U-235 Fig. 1 Maximum reactivity (k.) in Quad Cities fuel storage rack with postulated Boraflex gaps.

~

0 A) C" ES S)Y E RAC(S 0.95

' O.94 0.93 -

/

4 I

f /Vf 0.91

{

0 4 0.9 y

r 0.89 y

/

w 0.88 -

E 0.87 - aep 0.86 3 4

, 6

/,y' ,

0.84

< /

\

0.83 l

1.2 1.22 1.24 1.26 1.28 1.3 1.32 K-NflNRE N CORE GEON Fig. 2 Reactivity in fuel storage rack as a function of reactivity in standard core geometry.

6

A e the fuel initially contained a minimum of - 2. 5 wt. t gadolinium-oxide (Gd 23 0 ) in at least 5 fuel rods, or.

I e the discharged fuel- has attained a burnup of, 8 Mwd /kgU (averaged over the axial. height of the.

fuel assembly excluding the' natural uranium at ' the ' o ends),

I Alternatively, fuel may be safely stored if the highest j infinite multiplication ' f actor ( k,) at any time in the assembly )

burnup history .is equal to or less than 1.31, in the standard core geometry at 6 8 'F. . with no voids and without any control absorber present.

These criteria--and the results of this evaluation--are believed to be conservative for the following reasons.

i e The calculations assumed a uniform enrichment which gen-erally results in a higher reactivity than the actual case with distributed enrichments in BWR fuel.

e The calculations used a loading of 2.5% Gd 023 in 5 rods, which is less than that normally used, especially with the more highly enriched fuel.

e Residual gadolinium remaining at 8 Mwd /kgU was neglected.

o Burnup of the peak in reactivity (8 Mwd /kgU) neglects the I shift to higher burnup for the more highly enriched fuel (expected to be ~8.7 Mwd /kgU for 3.8% fuel).

l e The uncertainty allowance for gaps in the Boraflex was derived from a configuration with an extremely low proba-bility of occurring.

e The calculations assumed an infinite array of fuel at l

8 Mwd /kgU when, in reality, this burnup would occur only over a limited axial region and the lower reactivity on both sides would result in a lower k* for the actual fuel  !

assembly.

e the actual difference in average burnup in the fuel assemblies of a single fuel batch would result in the axial region of 8 Mwd /kgU occurring at different axial positions and further reduce the incremental reactivity

'effect of the postulated Boraflex gaps.

7 t _ .____-_____ _ _ _ -

i

+ i

't ,; i 3.0. ANALYTICAL METHODOLOGY 3.1: Fuel Assembly The fuel assembly used in the evaluation was the' General Electric 8 x 8 R fuel assembly with fuel rod characteristics as shown Lin Table 1. Parallel calculations established that, in the storage rack at 68'F, the 2-water-rod design described in Table 1 showed a slightly higher reactivity (nominal k, of 0.848 for 3.5% enrichment) at 8 Mwd /kgU than the 4-water-rod design (nominal k, of 0.846 for 3.5% enrichment). Similarly, burnup calculations were made for cases with 0%, 40%, and 60% void in the hot operating condition. On restart at 8 Mwd /kgU in the fuel rack at'68'F, the 60% void case gave the highest k, , approxi-mately 0.0013 ok greater than the 40% case. Since the 40% case is the nominal operating condition, the 0.0013 ok was included as an uncertainty in the final CASMO-2E reactivity determination.

The 0% void case gave a k, approximately 0.006 ok less than the reference case (where the burnup calculations had used 40% void) and is therefore not the limiting case.

3.2 Storage Rack Design The Quad cities spent fuel storage rack design, illustrated in Fig.- 3, is a honeycomb structure with 0.070-inch-thick Boraflex sandwiched between the two 0.075-inch stajnless steel walls of adjacent cells. The largest module in the spent fuel pool is a 16 by 16 array encompassing 256 cells. A nominal 3-inch water gap between the modules provides a flux-trap that ef fectively isolates the modules.

8 A. ___------_-__-----__-__---.--_._____-__--_-._---_---_____.-_.-_-__-a

s s

Table 1 FUEL ASSEMBLY DESIGN SPECIFICATIONS

• 8 x8R (Reference)

Fuel Rod Data Outside diameter, in. 0.483 Cladding thickness, in. 0.032 Cladding material Zr-2 Pellet density, gm UO 2 /cc 10.41 Pellet diarneter, in. 0.410 Enrichment, wt.% U-235 Variable Water Rod Data Outside diameter, in. 0.591 Wall thickness 0.030 Material 2r-2 Number per assembly 2 Fuel Assembly Data Number of fuel rods 62 Fuel rod pitch, in. 0.640 Fuel channel outside dimension, in. 5.438 Fuel channel wall thickness, in. 0.080 Fuel channel material Zr-4 Actual fuel assemblies have 6 inches of natural uranium at both ends of fuel rod.

l 9 l.

4

,- "" "[ ,,,,,

i .... . w . ., ,...

. e..le' 'T.'.'!!.

, ./a 00000000 00000000 00000000 000 0000 OO 09000 OO OOOOO O 000000 O 0000p0

. _ _ _ ._u ;

i- 7 p -

4m...

~

4 ,m .. .. .

[

1 Fig. 3 Cross-section of reference design storage cell for Quad Cities.

L 10

4:

's .

~

'Although, in ' the initial design, the Boraflex width was 5.B6 7

inches, shrinkage was ' assumed to reduce the width by 6.67%* to

l. 5.'47 inches, with a corresponding increase in effective boron concentration. Differential CASMO calculations indicated that these two opposing ef fects were nearly equal, and the small dif-ference was included as an uncertainty in the final CASMO-2E reactivity determination.

3.3 Geometric Model Since. infinite combinations of gap sizes and axial locations are- possible, a 4- by 4 array .(16 cells) centered around postulated Boraflex defects in a given axial plane was selected as the basic calculational unit. This array, as illustrated i

schematically in Fig. 4, includes 24 Boraflex sheets -in the center and 16 sheets along the periphery of the calculational unit. Reflective boundary conditions were used on all four sides of- the planar geometric model, which has the offeet of- repli-l cating the postulated defects throughout an infinite ~ erray of l storage cells. This is a very conservative model, especially when the probabilities of gaps of significant size occurring in adjacent Boraflex sheets are considered. (See NETCo supplement.)

The probabilities calculated in Attachment I are based upon the very conservative assumption that there will be shrinkage by

6. 67 % or 10 inches, with at least one axial gap occurring in every Boraflex sheet. Furthermore, the gaps of each size (in 1-inch increments) were assumed to have equal probability of occur-ring, in contrast to the Quad Cities' data that suggests the larger gap sizes have a much lower occurrence probability.

i

• Corresponds to 10-inch shrinkage in the 150-inch axial length (i.e., 6.67%).

11  !

1 1 j

l ',

• a 1

1 I I I I

\

l

m m  ;

I 3,

$ $ s

.4 v q  ;

4 M 4  :

L  ;

h w h k'  !

w U  :

6:s:G 29 : :N1 0 91 9: xN'J f6 ': 4. - :.J pc' s s tu ._ s1

- - n m e

.S :s s', '

N ss .

W 't! '1  : I e s s, ';

! 2 S 8  ;

J 4 e .

r New +3 . F2 c T: s 'ci -

t 0::r' -: J r.: ' tr a el 7

• m

-4 q

, .s s; ,

$ S; '

H, t q s

s; c .,

a as a x

. ,Q s

n r: : n- :a r, s m o, e ' :' u-:o ci cc m . a 3 -s1 g

's E

.f 3, ,

i '

a .s..a .

g i

l i l I i Fig. 4 Cross-sectional diagram of 4 by 4 cell arrangement for PDQ calculational unit.

12 1

1

t w -;

e i

In the largest module (a 16 by 16 array with 256 cells and 450 Boraflex sheets), the probability of two adjacent panels having 10-inch gaps at the same axial elevation is 10-4, meaning that, in the 450 Boraflex ' sheets of the largest module in the pool, coincident 10-inch gaps would be expected to occur only 0.045 times. Despite this low probability, coincident gaps were assumed to. occur with the 4 by 4 calculational unit centered around the assumed coincident failure. The probability of addi-tional 10-inch gaps at the' same axial elevation is given in Table 2.

Table 2 PROBABILITIES OF AXIALLY COINCIDENT BORAFLEX GAPS IN LARGEST (16 BY 16) MODULES 4-inch or Greater 10-inch Gaps Number of Coincident Proba- Occur , Proba- Occur ,

Gaps bility rences bility rences 2 0.119 53 1x10-4 0.045 3 0.0128 6 1x10~7 4.5x10-5 4 1.39x10-3 0.6 1x10-10 4.5x10-9 9 2.06x10-8 9x10-6 1x10-25 4.5x10-23 12 2,61x10~11 1 x10-'8 1x10-34 4.5x10-32 24 6.7x10-23 3 x10-20 1x10-70 4.5x10-69

• Number of occurrences expected in largest module (16 by 16 array).

The extremely low probability of multiple axially coincident gaps lends credibility to the 4 by 4 array chosen as the basic calcu-lational unit. Furthe rmore , further conservatism results from i 13

}

the fact that Boraflex gaps assumed to occur in the center of the basic calculational unit will be replicated sixteen times in the largest module.

4 3.4 .

Calculational Model The basic calculational model was CASMO-2E, a 2-dimensional transport theory code for assemblies, with depletion capability and shielded cross-sections for gadolinium burnable poison in specified fuel pins. Fuel burnup calculations were performed for typical operating conditions and the restart option in CASMO-2E at specified burnups used to calculate the infinite multipli-cation factor in the nominal spent - fuel storage cell at 68'F.

These calculations used a uniform enrichment initially, which in the past has invariably given a more conservative result (i.e.,

higher k, ) than for ue distributed enrichments normally used in BWR fuel.

CASMO-2E also has, as an option, the capability of producing multi-group dif f usion theory coefficients with transport theory corrected. constants for the strong absorber (Boraflex). These four-group dif fusion theory constants were then used in 2-dimen-sional PDQ calculations for variouc . assumed' configurations of Flux-weighted diffusion theory missing Boraflex sheets.

constants are an output edit option in PDO, which, in these cal-

' culations, was requested for subsequent use in the one-dimen- I sional SNEID code to synthesize a 3-dimensional representation of  !

the array. Independent 3-dimensional AMPX-KENO I4I

• calculations (a Monte Carlo code) with the 27-group SCALE cross-section library (5) were used for a few configuration.s to confirm the 3-dimensional synthesis model. In all cases, the KENO calculations _

I acronym for Standardized _C_ompute r Analysis for

' SCALE is an Licensing E_ valuation.

14

l l .

b- ,,

gave a lower k, value, which suggests that the synthesis model (CASMO-PDQ7-SNEID) may be slightly conservative.

Both CASMO-2E and the 27-group AMPX-KENO code package have been benchmarked against critical experiments appropriate for poisoned Jpent fuel storage . racks. Results . of these benchmark calculations are given in Appendix A.

Once the 3-D synthesis model had been used to calculate the reactivity effects of' a number of postulated configurations of Boraflex gaps, the resulting reactivities were then used to develop a conservative reactivity allowance, as a bounding condi-tion, for the consequences of postulated gaps in the Boraflex.

Once this' allowance had been developed, it was added to the other uncertainties (i.e., calculational and manufacturing tolerance effects) and combined with CASMO-2E results to determine the possible infinite multiplication factor for several highest values of initial enrichments. Uncertainties are summarized in Table 6. These CASMO-2E results, corrected for all uncertainties including the conservative upper bound due to Boraflex gaps, constitute the final result of the evaluation.

t f.

15 l

. 1

. 1 i

1 4.0 RESULTS I

4.1 Fuel Burnup Calculations 1 Puel burnup calculations were made for two different fuel assembly configurations (designs with 2 or 4 water rods in the center) and for soveral assumed levels of void content (0%, 40%,

and 60%). Using the restart option in CASMO-2E, the fuel assembly, at several selected burnup steps, can be analytically

" moved" into a typical spent fuel storage cell and the k, of an inf} nite array of such storage cells calculated. In these calcu- f lations, the temperature was set to 68'F and xenon was set to zero.

At temperatures above 68'P, the reactivity is lower.

Figure 5 illustrates the burnup dependent k, in the storage rack for fuel of 3.5% initial enrichment and with five fuel rods containing 2.5% gadolinium oxide (Gd 02 3). The peak in reactivity occurs at a burnup of 8 Mwd /kgU for this case. It may also be

)

noted that the k, of the fresh fuel is appreciably lower (because of the burnable poison), and the limiting reactivity is that occurring at the peak during burnup. At higher enrichments, or for greater gadolinium loading, the peak in reactivity would occur at a higher burnup, although, for the present evaluatirn, was neglected ( conserv ative) and a burnup of this effect 8 Mwd /kgU used as the design basis.

Results of the calculations with different fuel assembly configurations and average void content are listed in Table 3.

In these calculations, the void percentage refers to the void content in the hot operating conditions while the k, refers to Numerous calculations have determined that the xenon-free case yields the maximum shutdown reactivity of the fuel assembly and continuously de-that, in long-term storage, the reactivity creases due to decay of Pu-241 and growth of Am-241.

16

0 A) CIES SPEC E E_ RACKS 35t E - 5 RODS Of 251 Gd203 0.86 0.85

[h \ ,

0.64 ,

7

/ \ \

0.63

/ \

0.B?-

w / \

/ \

j 0.81 -

I i

0.8

\

0.79 -

0.78 0.77

\

0.76 0 2 4 6 8 10 12 14 16 18 20 FUEL BURA"JP, WD/KGU Fig. 5 Typical reactivity effects of fuel burnup on Quad Cities  ;

3 fuel (in storage rack).

17

. _ . ___ --._-__a

l lm Table 3 EFFECT OF ASSEMBLY CONFIGURATION AND AVERAGE VOID k, in Rack 0-Burnup @ 8 Mwd /kgU

~4 Water Rods, 40% void 0.8100 0.8464 2 Water Rods, 40% void 0.8142 0.8480 4 Water Rods, 0% void 0.8097 0.8421 2 Water Rods, 60% void NC 0.8493 At 68'F- for fuel of 3.5% initial enrichment containing 2.5%

Gd 023 in five fuel rods.

the cold, xenon-free, in-rack condition. The difference in reac-tivity for these cases is almost negligible, although the 2-water-rod case results in a slightly . higher in-rack k, and was used as the reference. For the' 60% void case, the 0.0013 ok higher value was included in the uncertainty addi-tion so that the final calculations of rack k, includes all reasonable void effects.

4.2 Two-Dimensional PDQ7 Calculations For the reference burnup calculation, the output edit option in CASMO-2E was invoked to obtain equivalent diffusion theory constants for the fuel assembly, external water, and Boraflex, the latter material being transport-theory-corrected using the H-option in CASMO. The PD07 calculations used the full 4 by 4 cell 18 i

array with 24 internal and 12 boundary Boraflex sheets expli-citly described in the 2-dimensional configuration. Table 4 summarizes.the infinite multiplication factors for a number of 2-D configurations of missing absorber sheets. This, however, does not reflect the cone? ion of the Quad Cities racks; only gaps in Table 4 INFINITE MULTIPLICATION FACTORS FROM PDQ7 CALCULATIONS WITH MISSING BORAFLEX SHEETS Case Missing Sheets (l) k,(2)

~

Reference None 0.8517 l 1 in-Center 1 0.8689 2 in-Line' I and 7 0.8795 3'in-Line 1, 7 & 12 0.8887 5 in-Line 1, 7, 12, 30 & 39 0.8992 4 Central 1-4 0.9095-12 Central 1-12 0.9949 24 Central 1-24 1.0832 1

All All 1.1240 /

(1) See Figure 4 for configuration and identification of the Boraflex . sheets assumed to be missing in the 2-D-calculations.

(2) k, for 3.5% initial enrichment, 2.5% Gd 023 in 5 rods, at 8 Mwd /kgU burnup.

• Sheets on boundary are half thickness due to the reflective boundary condition used in creating an infinite array.

19

l the material are present. The purpose of these calculations, l

summarized in Table 4, was to provide flux-weighted constants for the subsequent 3-D synthesis. However, the nature of the results do indicate substantial margins before reaching the maximum allowable reactivity. For example, at least four central full-length sheets could be completely missing and k, would still be less than 0.95.

4.3 Three-Dimensional Synthesis Flux-weighted diffusion theory constants, edited in the output of PDQ7, were used in the SNEID code,* a one-dimensional diffusion theory code. For conservatism, axial leakage was ne-glected and the axial region of missing Boraflex was assumed to be in the central location, since this is the most reactive posi-tion. Listed below (Table 5) are the results of calculations with diffusion constants edited from the PDQ7 runs cited in Table 4 above, assuming 10-inch axial region with missing Boraflex.

Calculations for several cases in Table 5 were made for smaller axially coincident gap sizes and the results are illustrated in Fig. 6. In all cases, the KENO Monte Carlo resulted in lower k, values suggesting that the 3-D synthesis is conservative ** (or the bias-corrected KENO calculation underpredicts reactivity with local regions of strong flux perturbations).

a t

• SNEIO is a one-dimensional diffusion theory code that has been benchmarked against 1-D PDQ7 calculations.

Special care was taken to avoid error due to source convergencegenerations in KENO, by checking the " number of initial skipped" to assure stable and consistent values of k,.

20

..1 t

III Table 5 THREE-DIMENSIONAL CALCULATIONS WITH 10-INCH REGIONS OF MISSING BORAFLEX Case ID 3-D Synthesis AMPX-KENO In 4 by 4 Calculational Unit (2) k, k, l

1) Reference - No Gaps 0.8517 0.8503i0.006 0.8532 NC

2) 1.10"-Gap in Center 0.8548 NC

3) 2-in-Line 10"-Gaps 0.8568 NC

4) 3-in-Line 10 "-Gaps 0.8597 NC 4 S) 5-in-Line 10"-Gaps .

6) 7 10"-Gaps in Two Levels (3) 0.8681 NC

7) 4 Central 10"-Gaps 'O.8630 0.8561i0.0055

8) 12 Central 10"-Gaps 0.9011 0.8874i0.0056 0.9503 NC

9) 24 Central 10"-Gaps

10) 10"- Gaps in All 0.9779 0.9712i0.0058 Boraflex Sheets 5 rods, (1)For fuel of 3.5% initial enrichment, 2.5% Gd 023 in burned to 8 Mwd /kgU.

(2)See also Fig. 4 and Table 4 for further identification of gap locations.

(3)Special case with three 10" gaps in center Boraflex sheets and two 10" gaps in axially contiguous regions, i.e., 30" of gap region.

I 4.4 Uncertainties in Criticality Calculations The objective of the CASMO-PDO-SNEID 3-D synthesis calcu- J lations was to establish a reasonable and conse rvative upper bound allowance (uncertainty) to be added to the basic CASMO i

l 21 i

1

)

_ J

5 1-O. A) C" S SW _ RAC(S 3.5% ENBCHWENT ML 1

0.99 0.98 0.97 7

0.96 0.95 a

0.94 i w

r

2 0.93

/g / /

Y s 0.92 y y 7 2

0.91 k

e 7 7

/ N/ - -

0.9 g/

c p 7 67' p /

0.89 + , -

x, # / /

4) 0.88 j, cr 7 0.87

/ / s c,v -

?/

/

. r / - __

_.y a 4 shee3h

, h/ ?D Q 0.85 0 2 4 6 8 10 12 CAP SIZE,INCHS h KENO CALCULATION Fig. 6 Variation in rack k,for gap sizes up to 10 inches in several configurations.

22

____ _ _J

calculations to define the maximum reactivity. in the spent fuel

. racks of. Quad Cities with gaps in the Boraflex absorber. This j uncertainty was additively combined with uncertainties .due to manufacturing tolerances and calculational uncertainties.

The uncertainties due to manufacturing tolerances were assumed to be the same as those previously eval- j uated (*0.0098 ok) and given in the Quad cities Licensing Document. However, depletion calculations could introduce addi-tional uncertainty. In the absence of critical experiment data with spent fuel, the uncertainty in burnup calculations.must be determined from other considerations. One method that has been used to estimate burnup uncertainty is to assume a value equal to 0.0005 times the burnup, which, in this case, would' be ~0.004 Ak at 8 Mwd /kgU. However, some additional uncertainty could possibly be associated with gadolinium cross-section.

Therefore, for the present analysis, it was assumed that setting the residual gadolinium content at 8 Mwd /kgU to zero would be conservative and adequate to compensate for all uncertainties due to the burnup analysis (equals 0.0111 ok) .

Based on the 3-D synthesis calculations, the uncertainty in reactivity due to 10-inch gaps in four adjacent Boraflex sheets

.at the same axial plane is 0.0113 Ak (see Table 5 and Fig. 6).

While this uncertainty might be considered a reasonably conser-vative estimate, the allowance for Boraflex-gap uncertainty was arbitrarily increased

• to 0.040 ak as a very conservative upper bound estimate and to allow for other possible configurations not specifically calculated. This upper bound estimate has an extremely low probability of occurring , correspor' ding (see Fig.

6) to the following:

• Also assumed to include the very small correction (+0.0038 Ak uncertainty) for Boraflex shrinkage in width and for the possible effect of operating void content.

23

a e app ten 10-inch central gaps--probability of 10-gximately

, or e twelve 8-inch central. gaps--probability of 10-33, or e twenty-four central 5-inch gaps--probability of 10-63, or e concurrently in all sheets--probability of 4-i gh10-b gaps Calculations with assumed Boraflex gaps larger than 10 inches indicate that the 0.040 Ak' allowance is equivalent to approxi-mately 35 inches of gap occurring at the same axial plane in the central four sheets. As a further example, fuel of 3.5% initial enrichme'nt .would have a maximum k, , ' including 0.0529.3k for uncertainties, of 0.9113 at .8 Mwd /kgU burnup. For this enrich-ment and burnup, the .Ouad cities L racks could safely accommodate 1

' Boraflex gaps up to 6 inches occurring at the same elevation everywhere in- the pool, without ' exceeding the limiting k, of 0.95 and would not be critical for 10-inch gaps everywhere.

The considerations discussed above confirm that the 0.040 Ak allowance for gaps in the Boraflex is a very conser-vative', low-probability, upper bound of the reactivity effect.

Tabic 6 shows the uncertainties f rom all ef f ects, combined addi-t'.vely rather than statistically, for additional conservatism.

Table 6 COMBINED UNCERTAINTIES IN CRITICALITY SAFETY ANALYSIS 4

Uncertainty Ak Manuf acturing tolerances *0.0098 CASMO bias and uncertainty *0.0031 l

l Boraflex gap allowance 0.040 Total +0.0529 l

24 V _ - _ _ _ - _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ - _ _ - _ _ _ - - _ _ _ -

l 4.5 Capability of Fuel Storage Rack Once the total uncertainty had been determined (0.0529 Ak), a series of CASMO-2E calculations were made for several different initial enrichments. At the same time, calculations were made for the fuel assemblies in the

" standard" core geometry defined as fuel assemblies on a 6-inch lattice spacing at 68'F without void or control absorber present. The calculations at: 8 Mwd /kgU were made with the resid-ual gadolinium set to zero. Results of these calculations are given in Table 7 and summarized in Figs. 1 and 2. At the highest initial enrichment considered (3.8%), the maximum k, is 0.9314, which is still nearly 2% Ak below the limit of 0.95. Thus, the Quad Cities spent fuel storage racks can safely accommodate fuel up to 3.8% initial enrichment, provided the fuel contained at least 2.5% Gd 023 in a minimum of 5 rods or had at.tained an aver-age discharge burnup of 8 Mwd /kgU or more (excluding the natural uranium axial blanket).

I l

25  ;

I l

l

7___ _

9 d

e I

l Table 7 CALCULATED k VALUES WITH BORAPLEX GAPS IN THE QUAD CITIES STORAGE RACKS I2I k, @ Zero Burnup (1) k, @ 8 Mwd /kgU Initial Enrichment Core Geom. Rack Geom. Core Geom. Rack Geom.

3.19% 1.2069 0.8420 1.2616 0.8880 3.4% 1.2276 0.8594 1.2806 0.9040 3.5% 1.2366 0.8671 0.2894 0.9113 3.6% 1.2455 0.8745 1.2973 0.9182 3.8% 1.2621 0.8887 1.3126 0.9314 (1) Fresh fuel calculations assumed 2.5% Gd 023 in 5 fuel rods.

I2) Calculations at 8 Mwd /kgU set residual Gd to zero and include 0.0529 ok uncertainties.

26

~

9 REFERENCES

1. A. Ahlin, M. Edenius, H. Haggblom, "CASMO - A Fuel Assembly Burnup Program," AE-RF-76-4158, Studsvik report (proprietary).

A. Ahlin and M. Edenius, "CASMO -A Fast Transport Theory Depletion Code for LWR Analysis," ANS Transactions, Vol. 26,

p. 604, 1977.

M. Edenius et al., "CASMO Benchmark Report," Studsvik/RF-78/6293, Aktiebolaget Atomenergi, March 1978.

" CASMO-2 E Nuclear Fuel Assembly Analysis, Application Users Manual," Rev. A, Control Data Corporation, 1982.

2. W. R. Cadwell, PDQ7 Reference Manual, WAPD-TM-678, Bettis Atomic Power Laboratory, January 1967.

3. SNEID is a one-dimensional diffusion theory code in 4 groups, developed for the IBM-PC-AT and benchmarked against PDQ7.

4. Green, Lucious, Petrie, Ford, White, Wright, "PSR-63/AMPX-1 (code package), AMPX Modular Code System for Generating Coupled Multigroup Neutron-Gamma Libraries from ENDF/B,"

ORNL-TM-3706, Oak Ridge National Laboratory, March 1976.

L. 'M . Petrie and N. F. Cross, " KENO-IV, An Improved Monte Carlo Criticality Program," ORNL-4938, Oak Ridge National Laboratory, November 1975.

5. R. M. Westfall et al., " SCALE: A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluation," NUREG/CR-0200, 1979.

W. E. Ford, III et al., "A 218-Neutron Group Master Cross-section Library for Criticality Safety Studies," ORNL/TM-4 ,

1976.

6. M. G. Natrella, " Experimental Statistics," National Bureau of Standards, Handbook 91, August 1963.

27

h-l-  ? e' i e t

~b l .r i

f e

t

^

APPENDIX A BENCHMARF CALCULATIONS l

e e

1 i

i 1

l 1

1 A-1 I I

_ _ - - _ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - _ .- )

l' i

l.  !

1. INTRODUCTION AND

SUMMARY

The objective of this benchmarking study is to verify both the AMPX (NITAWL)-KENO (Refs. I and 2) methodology with the 27- i group SCALE cross-section library (Refs. 3 and 4) and the CASMO-2E code (Refs. 5, 6, 7, and 8) for use in criticality calcula- l tions of high density spent fuel storage racks. Both calcu-lational methods are based on transport theory and have been benchmarked against critical experiments that simulate typical spent fuel storage rack designs as realistically as possible.

Results of these benchmark calculations with both methodologies are consistent with corresponding calculations reported in the literature and with the requirements of Regulatory Guide 3.41, Rev. 1, May 1977.

Results of these benchmark calculations show that the 27-group (SCALE) AMPX-KENO calculations consistently underpredict the critical eigenvalue by 0. 0106 i 0. 0048 Ak (with a 95% proba-bility at a 95% confidence level) for critical experiments (Ref.

9) selected to be representative of realistic spent fuel storage rack configurations and poison worths. Similar calculations by Westinghouse (Ref. 11) suggest a bias of 0.012

• 0.0023, and the results of ORNL analyses of 54 relatively " clean" critical experiments (Ref. 12) show a bias of 0.0100 i 0.0013.

i Similar calculations with CASMO-2E for clean critical experiments resulted in a bias of 0.0013 i 0.0018 (95%/95%).

CASMO-2E and AMPX-KENO intercomparison calculations of infinite arrays of poisoned cell configurations show very good agreement and suggest that a bias of 0.0013 i 0.0018 is the reasonably expected bias and uncertainty for CASMO-2E calculations.

Validation of Calculational Methods for Nuclear Criticality Safety. (See also ANSI N16.9-1975.)

A-2

'O The benchmark calculations reported here indicate that either the 27-group (SCALE) AMPX-KENO or CASMO-2E calculations are acceptable for criticality analysis of high density spent fuel' storage racks. The preferred methodology, however, is to perform independent calculations with both code packages and to utilize the higher, more conservative value for the reference design infinite multiplication factor.

2. AMPX (NITAWL)-KENO BENCHMARK CALCULATIONS Analysis of a series of Babcock & Wilcox (B&W) critical experiments (Ref. 9), which include some with absorber sheets typical. of a poisoned spent fuel rack, is summarized in Table 1, as calculated with AMPX-KENO using the 27-group SCALE cross-section library and the Nordheim resonance integral treatment in NITAWL. The mean for these calculations is 0.9694

• 0.0019, conservatively assuming the larger standard deviation calculated from the kegg values. With a one-sided tolerance factor corresponding to 95% probability at a 95% confidence level (Ref.

10), the calculational bias is +0.0106 with an uncertainty of

• 0.0048.

Similar calculational deviations reported by Westinghouse (Ref. 11) ara also shown in Table 1 and suggest a bias of 0.012

• 0.0023 (95%/95%). In addition, ORNL (Ref. 12 ) has analyzed some 54 critical experiments using the same methodology, obtaining a mean bias of 0.0100

• 0.0013 (95%/95%). These published results are in good agreement with the results obtained in the present analysis and lend further credence to the validity of the 27-group AMPX-KENO calculational model for use in criticality analy-sis of high density spent fuel storage racks. Variance analysis of the data in Table 1 suggests the possibility that an unknown factor may be causing a slightly larger variance than might be expected from the Monte Carlo statistics alone. However, such a A-3

I .

Table 1 RESULTS OF 27-GROUP (SCALE) AMPX-KENO CALCULATIONS OF B&W CRITICAL EXPERIMENTS i

Westinghouse Experiment Calculated Calculated-meas.

Number kegg a kegg I 0.9889 *0.0049 -0.008 II 1.0040 *0.0037 -0.012 III 0.9985 *0.0046 -0.008 IX III 0.9924 *0.0046 -0.016 X 0.9907 *0.0039 -0.008 XI 0.9989 10.0044 +0,002 XII 0.9932 i0.0046 -0.013 XIII 0.9890 t0.0054 -0.007 XIV 0.9830 *0.0038 -0.013 XV 0.9852 *0.0044 -0.016 XVI 0.9875 *0.0042 -0.015 XVII 0.9811 *0.0041 -0.015 XVIII 0.9784 *0.0050 -0.015 XIX 0.9888 *0.0033 -0.016 XX 0.9922 AO.0048 -0.011 XXI 0.9783 *0.0039 -0.017 Mean 0.9894 *0.0011(2) -0.0120 i 0.0010 Bias 0.0106 *0.0019(3) 0.0120

• 0.0010 Bias (95%/95%) 0.0106 i0.0048 0.0120 i 0.0023 Maximum Bias 0.0154 0.0143 i

(1) Experiments IV through VIII used B 4 C pin absorbers and were not considered representative of poisoned storage racks.

(2) Calculated from individual standard deviations.

(3) Calculated from ke gg values and used as reference.

A-4

1 1

l factor, if one truly exists, is too small to be resolved on the basis of critical-experiment data presently available. No trends in keff with intra-assembly water gap, with absorber sheet-reactivity worth, or with soluble poison concentration were identified.

l

3. CASMO-2E BENCHMARK CALCULATIONS 3.1 GENERAL The CASMO-2E code -is a multigroup transport theory code j utilizing transmission probabilities to accomplish two-dimen-sional calculations of reactivity and depletion for BWR and PWR fuel assemblies. As such, CASMO-2E is well-suited to the criti-cality analysis of spent fuel storage racks, since general practice is to treat the racks as an infinite medium of storage cells, neglecting leakage effects.

CASMO-2E is closely analogous to the EPRI-CPM code (Ref. 13) q and has been extensively benchmarked against hot and cold crit-ical experiments by Studsvik Energiteknik (Refs. 5, 6, 7, and 8). Reported analyses of 26 critical experiments indicate a mean k,gg of 1.000 i 0.0037 (lo). Yankee Atomic (Ref. 14) has also reported results of extensive benchmark calculations with CASMO-2E. Their analysis of 54 Strawbridge and Barry critical experi-ments (Ref. 15) using the reported buckling indicates a mean of 1

0.9987 i 0.0009 (lo), or a bias of 0.0013

• 0.0018 (with 95%

probability at a 95% confidence level). Calculations were repeated for' seven of the Strawbridge and Barry experiments

• Ssignificantly large trends in kef with water gap and with ab- I sorbersheetreactivityworthhavebeenreported (Ref. 16) for AMPX-KENO calculations with the 123-group GAM-THERMOS library.

A-5

L *

.. j i

L I

selected at' random, yielding a mean keff of 0.9987 i 0.0021 (la), j thereby confirming that the cross-section library and analytical methodology being used for the present calculations are the same  ;

as those used in the Yankee analyses. Thus, the expected bias

'for CASMO-2E in the analysis'of " clean" critical experiments is 0.0013

• 0.0018 (95%/95%).

i 3.2 BENCHMARK CALCULATIONS i

l CASMO-2E benchmark calculations have also been made for the f i

B&W series of critical experiments with absorber sheets, simu-l-

lating high density. spent fuel storage racks. However, CASMO-2E, i L

as an assembly ' code, cannot directly represent an entire core' l configuration

• without introducing uncertainty due to reflector constants and the appropriateness of their spectral weighting.

For this reason, the poisoned cell configurations of the central assembly, as calculated by CASMO-2E, were benchmarked against corresponding calculations with the 27-group (SCALE) AMPX-KENO  !

! code package. Results of this comparison are shown in Table 2.

Since the differences are well within the normal KENO statistical variation, these calculations confirm the validity of CASMO-2E calculations for the typical high density poisoned spent fuel rack configurations. The differences shown in Table 2 are also consistent with a blas of 0.0013 i 0.0018, determined in Section 3.1 as the expected bias and uncertainty of CASMO-2E calcula-tions.

• Yankee has attempted such calculations (Ref, 14) using CASMO-2E-generated constants in a two-dimensional, four-group PDQ model, obtaining a mean kegg of 1.005 for 11 poisoned cc.ses and 1.009 for 5 unpoisoned cases. Thus, Yankee benchmark calculations suggest that CASMO-2E tends to slightly overpredict reactivity.

A-6

- - - - - _ o

L t

s L"

Table 2 RESULTS OF CASMO-2E BENCHMARK (INTERCOMPARISON) CALCULATIONS k,III

..B&W Experiment No.(1) AMPX-KENO (2) CASMO-2E Ak 1

XIX 1.1203.* 0.0032 1.1193 0.0010 XVII 1.1149

• 0.0039 1.1129 0.0020 XV 1.1059

• 0.0038 1.1052 0.0007 Interpolated (3) 1.1024 i-0.0042 1.1011 0.0013.

XIV~ 1.0983

• 0.0041 1.0979 0.0004' XIII 1 0992

• 0.0034 1.0979 0.0013 Mean i 0.0038 0.0011 Uncertainty *0.0006-BWR fuel rack 0.9212

• 0.0027 0.9218 -0.006 (1)Infinitearrayohcentralassembliesof9-assemblyB&Wcriti-cal configuration (Ref. 9).

(2)k ' from AMPX-KENO corrected for bias of 0.0106 ok.

(3 )IEtterpolated. f rom - Fig. 28 of Ref. 9 for soluble boron concen-tration at critical condition.

A-7

t

,: a; REFERENCES TO APPENDIX A

1. Green, Lucious, Petrie, Ford , Whito , Wright, "PSR-63/AMPX-1 (code package), AMPX Modular ' Code. System for Generating Coupled Multig roup Neutron-Gamma Libraries from- ENDF/B,"

ORNL-TM-3706, Oak Ridge National Laboratory, March 1976.

2. L. M. Petrie and N. F. Cross, " KENO-IV, An Improved Monte Carlo Criticality Program," ORNL-4938, Oak Ridge National Laboratory, November 1975.

3. R. M. Westfall et al . ', " SCALE: A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluation," NUREG/CR-0200, 1979.

4. W. E. Ford, III et al., "A ' 218-Neutron Group Master Cross-section Library for Criticality Safety Studies," ORNL/TM-4, 1976.

5. A. Ahlin, M. Edenius, H. Haggblom, "CASMO - A Fuel Assembly Burnup Program,"- AE-RF-76-4158, Studsvik report (proprietary).

6. A. .Ahlin and M. Edenius, " CASMO - A Fast Transport Theory Depletion Code for LWR Analysis," ANS Transactions, Vol. 26,

p. 604, 1977.

7. M. Edenius et al., "CASMO Benchmark Report," Studsvik/RF-78/6293, Aktiebolaget Atomenergi, March 1978.

8. " CASMO-2 S Nuclear Fuel Assembly Analysis, Application Users.

Manual," Rev. A, Control Data Corporation, 1982.

9. M. N. Baldwin et al., " Critical Experiments Supporting Close Proximity Water Storage of Power Reactor Fuel," BAW-1484-7, The Babcock & Wilcox Company, July 1979.

10. M. G. Natrella, Experimental Statistics, National Bureau of Standards, Handbook 91, August 1963.

.11. B. F. Cooney et al., " Comparisons of Experiments and Calculations for LWR Storage Geometries," Westinghouse NES, ANS Transactions, Vol. 39, p. 531, November 1981.

12. R. M. Westfall and J. R. Knight, " Scale System Cross-section Validation with Shipping-cask Critical Experiments," ANS Transactions, Vol. 33, p. 368, November;1979.

13. "The EPRI-CPM Data Library," ARMP Computer Code Manuals, Part II, Chapter 4, CCM3, Electric Power Research Institute, November 1975.

A-8

.. i 1

REFERENCES TO APPENDIX A (Continued)

14. E. E. Pilat, " Methods for the Analysis of Boiling Water Reactors (Lattice Physics)," YAEC-1232, Yankee Atomic Electric Co., December 1980.

15. L.;E. Strawbridge and~R..F. Barry, " Criticality Calculations f or Uniform, Water-moderated Lattices," Nuclear Science and Engineering , Vol. 23, p. . 58, September 1965.

16. 'S. E. Turner and M. K. Gurley, " Evaluation of AMPX-KENO Benchmark Calculations for High Density Spent Fuel Storage Racks," Nuclear Science and Engineering, 80(2): 230-237, February 1982.

A-9

_ _ _ _ - _ _ _